TOPICS IN APPLIED MATHEMATICS-22M:321 (MATH:7830)

Quantum Mechanics (foundations, practical models, and algorithms)

SPRING SEMESTER 2011


SYLLABUS

Course meeting times: 4:30-5:20 MWF. Standard out-of-class preparation is at least six hours.

Course meeting place: 214 MLH

Prerequisites: None, although a course on ordinary differential equations such as 22M:213, 22M:214 is recommended.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 10:30-noon. I will also be available at other times. Just drop by my office or send me an e-mail to make an appointment.

Telephone: (319)-335-0898

Fax: (319)-335-0627

E-mail address: ljay@math.uiowa.edu

Mailbox: in Mailroom 15 MLH

Course web page: Information about the course will be given in http://www.math.uiowa.edu/~ljay/m321_11.html. Students are responsible for checking regularly this course web page.

Goals and objectives of the course: This course is at a graduate level and it is assumed that you can work along the course in an independent fashion. This is a topics course on quantum mechanics from its theoretical foundations to practical models and algorithms. No reason to be afraid since we will take a gentle approach. Even the famous Nobel prize winner Richard Feynman once said: "I think I can safely say that nobody understands quantum mechanics". That does not mean what we cannot try to do some quantum mechanics. We will follow several textbooks and the pace will be quite sustained. At the end of the semester we might not see our world in the same way. A lot of contemporary pure and applied mathematics has been developed for the purpose of giving strong foundations to quantum mechanics. We will discuss of course the main mathematical concepts of quantum mechanics. We will also discuss some modeling and numerical aspects (e.g., Hartree-Fock approximations, how to practically calculate matrix exponentials of large matrices, etc.). This course should be of interest even for those who only like pure mathematics. This is a course really dedicated to mathematics (pure or applied) students since we will not do much physics or chemistry. This course is mostly based on reading. We will cover as many topics as possible, but of course several of them will be skipped due to time limits.

Textbooks:

  • (FY) Required: Lectures on Quantum Mechanics for Mathematics Students by L.D. Faddeev and O.A. Yakubovskii, American Mathematical Society, Student Mathematical Library, vol. 47, 2009, ISBN-10: 0-8218-4699-X, ISBN-13: 978-0-8218-4699-5, list price: $39 (the bookstore sells it at $41.60!). Library reference: Engineering Library QC174.125 .F3213 2009 . The book on amazon.com.
  • (GS) Required: Mathematical Concepts of Quantum Mechanics by Stephen J. Gustafson and Israel Michael Sigal, Springer, Universitext, 2003, ISBN-10: 3540441603, ISBN-13: 978-3540441601, list price: $69.95. The book on amazon.com.
  • (L) Required: From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis by Christian Lubich, European Mathematical Society, 2008, ISBN-10: 3037190671, ISBN-13: 978-3037190678, list price: $41.60 (32 Euros). The book on amazon.com.
  • (T) Recommended: Quantum Mechanics for Mathematicians by Leon A. Takhtajan, American Mathematical Society, Graduate Studies in Mathematics, 2008, ISBN-10: 0821846302, ISBN-13: 978-0821846308, list price: $69.00. Library reference: Main Math Collection QC174.12 .T345 2008. The book on amazon.com.
  • Class procedures: The majority of each class period will be lecture oriented. I or you will present the material and we will discuss it in class and help each other understand what we are reading through lively discussions (hopefully!).

    Grading procedures: There will be no mandatory homework. The grade will be based on attendance (30%) and some level of participation (70%). Assessing your level of participation of course may be a bit subjective and I will try to be as fair as possible in keeping track of your participation level. You can volunteer to give a presentation on some proofs or topics (it could be 5 minutes long or longer and I would like to see your material in advance). You can show me the work that you have done. You will be asked to look at some proofs or problems from the books. The more you do and the better for your level of participation. Please be proactive. Your participation in class is also important. The more you participate to discussions and the better for your grade. Just attending every class and sitting silently the whole semester without doing any work will earn you a grade of C.

    No final examination.

    Add or drop: Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences.

    Cross enrollments: Details of the University policy of cross enrollments may be found at: http://www.uiowa.edu/~provost/deos/crossenroll.doc.

    Notes to student: The Department of Mathematics has offices in 14 MLH. To make an appointment to speak with the Chair of the Department, call 335-0714 or contact the Departmental Secretary in 14 MLH.


    The College of Liberal Arts and Sciences Policies and Procedures

    The CLAS policy statements have been summarized from the web pages of the College of Liberal Arts and Sciences.

    Administrative Home: The College of Liberal Arts and Sciences is the administrative home of this course and governs matters such as the add/drop deadlines, the second-grade-only option, and other related issues. Different colleges may have different policies. Questions may be addressed to 120 Schaeffer Hall, or see the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/.

    Electronic Communication: University policy specifies that students are responsible for all official correspondences sent to their University of Iowa e-mail address (@uiowa.edu). Faculty and students should use this account for correspondences. (Operations Manual, III.15.2 at http://www.uiowa.edu/~our/opmanual/iii/15.htm#152/ Scroll down to k.11.)

    Accommodations for Disabilities: A student seeking academic accommodations should first register with Student Disability Services and then meet privately with the course instructor to make particular arrangements. See http://www.uiowa.edu/~sds/ for more information.

    Academic Fraud: Plagiarism and any other activities when students present work that is not their own are academic fraud. Academic fraud is a serious matter and is reported to the departmental DEO and to the Associate Dean for Undergraduate Programs and Curriculum. Instructors and DEOs decide on appropriate consequences at the departmental level while the Associate Dean enforces additional consequences at the collegiate level. See the CLAS Academic Fraud section of the Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#2.

    CLAS Final Examination Policies: Final exams may be offered only during finals week. No exams of any kind are allowed during the last week of classes. Students should not ask their instructor to reschedule a final exam since the College does not permit rescheduling of a final exam once the semester has begun. Questions should be addressed to the Associate Dean for Undergraduate Programs and Curriculum.

    Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit the instructor, then the course supervisor, and then the departmental DEO. Complaints must be made within six months of the incident. See the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#5.

    Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. All members of the UI community have a responsibility to uphold this mission and to contribute to a safe environment that enhances learning. Incidents of sexual harassment should be reported immediately. See the UI Comprehensive Guide on Sexual Harassment at http://www.uiowa.edu/~eod/policies/sexual-harassment-guide/index.html for assistance, definitions, and the full University policy.

    Reacting Safely to Severe Weather: In severe weather, class members should seek appropriate shelter immediately, leaving the classroom if necessary. The class will continue if possible when the event is over. For more information on Hawk Alert and the siren warning system, visit the Public Safety web site at http://www.uiowa.edu/~pubsfty/intlinks.htm.

    Resources:

    Student Classroom Behavior: The ability to learn is lessened when students engage in inappropriate classroom behav- ior, distracting others; such behaviors are a violation of the Code of Student Life. When disruptive activity occurs, a University instructor has the authority to determine class- room seating patterns and to request that a student exit immediately for the remainder of the period. One-day suspensions are reported to appropriate departmental, collegiate, and Student Services personnel (Office of the Vice President for Student Services and Dean of Students).

    University Examination Policies: Missed exam policy. University policy requires that students be permitted to make up examinations missed because of illness, mandatory religious obligations, certain University activities, or unavoidable circumstances. Excused absence forms are available at the Registrar web site: http://www.registrar.uiowa.edu/forms/absence.pdf

    Final Examinations: An undergraduate student who has two final examinations scheduled for the same period or more than three examinations scheduled for the same day may file a request for a change of schedule before the published deadline at the Registrar's Service Center, 17 Calvin Hall, 8-4:30 M-F, (384-4300).